An apparatus for the performance of the above-named method is known from EP-A-0205206. In this known apparatus, the forage is pressed between two belts, guided on a plurality of drive rolls or deflecting rolls, one of which belts exhibits a perforated structure. In this way, a part of the liquid present in the stalks is expressed from the green mass so that the subsequent drying process up to the harvesting of the hay is shortened. What is more, the residual liquid remaining in the stalks can evaporate more rapidly by virtue of the fact that the surface of the stalks is fanned out by means of the pressing process. A forage compacted into a mat of stalk material exits the pressing elements, the density and the cross section of said mat of stalk material depending on the quantity of forage mowed or gathered in each case. In this method, the mass of stalk material needed for producing a uniformly thick and inherently stable mat is lacking if the inventory of stalk material is sparse, especially at field entries and when margins are mowed out. On the other hand, the mat of stalk material exits the known apparatus in a disordered form having little stability; that is, on exiting the machine and correspondingly being laid down on the stubble, the mat of stalk material breaks up into small elements that are not saved well in a subsequent harvesting operation. The losses of brittle material are therefore very great. Furthermore, the drying process is prolonged by virtue of the fact that blade and stalk portions of the forage are not adequately mixed together.